Finite Group Databasebeta

← C2×#19145931 #25969401

Subgroups — C2×#19145931 #25969401

Order 11008.

1930 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic, complemented
2C2×#14583434C211yesmaximal, characteristic
3#19145931C2116yesmaximal, direct product factor
4C2×#14583203C211yesmaximal, characteristic, complemented
5C2×#14583183C211yesmaximal, characteristic, complemented
6C2×#14583178C211yesmaximal, characteristic, complemented
7C2×#14583141C211yesmaximal, characteristic, complemented
8C2×#14583139C211yesmaximal, characteristic, complemented
9C2×#14583131C211yesmaximal, characteristic
10C2×#14583129C211yesmaximal, characteristic
11C2×#14583122C211yesmaximal, characteristic, complemented
12C2×#14583121C211yesmaximal, characteristic, complemented
13C2×#14583108C211yesmaximal, characteristic, complemented
14C2×#14583103C211yesmaximal, characteristic, complemented
15C2×C4⋊C8×D43C211yesmaximal, characteristic, complemented
16C2×C43×#479C211yesmaximal, characteristic, complemented
17C22×Dic172C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583453—24no—
24#14583453C2218yescomplemented
25C2×#13063324C2211yescharacteristic
26C2×#13063323C2211yescharacteristic
27#14583434—24no—
28#14583434C2218yes—
29C2×#13063320—21no—
30C2×#13063315—21no—
31C2×#13063313C2211yescharacteristic
32C2×#13063310—21no—
33C2×#13063305C2211yescharacteristic
34C2×#13063305C2211yescharacteristic
35C2×#13063303—21no—
36C2×#13063301C2211yescharacteristic
37C2×#13063300C2211yescharacteristic
38C2×C4×Dic86—21no—
39C2×C4×Dic86C2211yescharacteristic
40C2×#13063290C2211yescharacteristic
41C2×#13063287—21no—
42C2×#13063287C2211yescharacteristic
43C2×#13063283—21no—
44C2×#13063282—21no—
45C2×C42×D43C2211yescharacteristic
46#14583203C2218yescomplemented
47#14583183C2218yescomplemented
48#14583178C2218yescomplemented
49#14583141C2218yescomplemented
50#14583139C2218yescomplemented
51#14583131C2218yes—
52#14583129C2218yes—
53#14583122C2218yescomplemented
54#14583121C2218yescomplemented
55#14583108C2218yescomplemented
56#14583103C2218yescomplemented
57C2×#13063258C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×C4⋊(C43⋊C8)C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C4⋊C8×D43C2218yescomplemented
63C2×#13063250C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063248C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063245C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#479C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×D172—21no—
81C22×D172C2311yescharacteristic
82C22×C4×D43—21no—
83C22×C4×D43D411yescharacteristic
84C22×C4×D43D411yescharacteristic
85C22×C4×D43C2311yescharacteristic
86C2×Dic172—42no—
87C2×Dic172C2314yes—
88C2×#10621885—42no—
89C2×#10621885C2314yes—
90C2×#10621873—42no—
91C2×#10621873C2314yes—
92C2×#10621884—42no—
93C2×#10621884C2314yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C2×C8×D43—42no—
97C2×C8×D43—42no—
98C2×C8×D43C2314yes—
99C2×C8×D43C2314yes—
100#13063324—22no—
101#13063324C2314yes—
102#13063323—22no—
103#13063323C2314yes—
104#13063320—28no—
105#13063315—28no—
106#13063313—22no—
107#13063313C2314yes—
108#13063310—28no—
109#13063305—22no—
110#13063305—22no—
111#13063305C2314yes—
112#13063305C2314yes—
113#13063303—28no—
114#13063301—22no—
115#13063301C2314yes—
116#13063300—22no—
117#13063300C2314yes—
118C4×Dic86—22no—
119C4×Dic86—28no—
120C4×Dic86C2314yes—
121#13063290—22no—
122#13063290C2314yes—
123#13063287—28no—
124#13063287—22no—
125#13063287C2314yes—
126#13063283—28no—
127#13063282—28no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149C42×D43D414yes—
150C42×D43C2314yes—
151#13063258C2314yes—
152#13063256C2314yes—
153C4⋊(C43⋊C8)C2314yes—
154Dic43⋊C8C2314yes—
155Dic43⋊C8C2314yes—
156#13063250C2314yes—
157#13063248C2314yes—
158#13063248C2314yes—
159#13063248C2314yes—
160#13063247C2314yes—
161#13063245C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165#125×C43—22no—
166#125×C43C2314yes—
167C4×Q8×C43—22no—
168C4×Q8×C43C2314yes—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C42×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#107×C43C2314yes—
178#106×C43C2314yes—
179C4⋊C8×C43C2314yes—
180#103×C43C2314yes—
181#103×C43C2314yes—
182C23×D43—21no—
183C23×D43C2×D411yescharacteristic
184C2×Q8×C43—21no—
185C2×Q8×C43—22no—
186C2×Q8×C43—22no—
187C2×Q8×C43C2412yes—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200C22×Dic43C2×D411yescharacteristic
201C2×D172—21no—
202C2×D172—24no—
203C2×D172—22no—
204C2×D172—22no—
205C2×D172—44no—
206C2×D172C2412yes—
207C2×C4×D43—22no—
208C2×C4×D43—22no—
209C2×C4×D43—24no—
210C2×C4×D43—24no—
211C2×C4×D43—24no—
212C2×C4×D43—44no—
213C2×C4×D43C2×D412yes—
214C2×C4×D43C2×D414yes—
215C2×C4×D43C2×D414yes—
216C2×C4×D43C2412yes—
217C2×Dic86—22no—
218C2×Dic86—22no—
219C2×Dic86—22no—
220C2×Dic86—22no—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—24no—
224C2×Dic86—44no—
225C2×Dic86C2412yes—
226C2×Dic86C2412yes—
227C2×C8×C43—22no—
228C2×C8×C43—22no—
229C2×C8×C43C2412yes—
230C2×C8×C43C2412yes—
231C4⋊C4×C43—24no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C4⋊C4×C43C2412yes—
240C42×C43—24no—
241C42×C43C2×D412yes—
242C42×C43C2412yes—
243#10621885—44no—
244#10621884—44no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252C4⋊Dic43—21no—
253C4⋊Dic43—24no—
254C4⋊Dic43—24no—
255C4⋊Dic43C2412yes—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43C2×D412yes—
265C4×Dic43C2×D414yes—
266C4×Dic43C2×D414yes—
267C4×Dic43C2412yes—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—22no—
270C2×C43⋊C8C2412yes—
271C2×C43⋊C8C2412yes—
272Dic172—44no—
273#10621873—44no—
274C8×D43—44no—
275C8×D43—44no—
276C23×C43C22×D411yescharacteristic
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43#13714yes—
284C22×D43C22×D412yes—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—42no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43C22×D412yes—
299C2×C4×C43C22×D412yes—
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43H(5,𝔽2)12yes—
302C2×C4×C432−1+412yes—
303C2×C4×C43C2511yescharacteristic
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43#13514yes—
313C2×Dic43C22×D412yes—
314C2×Dic43C22×D412yes—
315C2×Dic43C22×D412yes—
316D172—22no—
317D172—22no—
318D172—48no—
319D172—42no—
320C4×D43—28no—
321C4×D43—24no—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—28no—
325C4×D43—48no—
326Dic86—22no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86—42no—
331Dic86—42no—
332Dic86—48no—
333C8×C43—22no—
334C8×C43—22no—
335C43⋊C8—22no—
336C43⋊C8—22no—
337C2×#3248—431nomaximal, Sylow
338C22×C43#53712yes—
339C22×C43C2×#13512yes—
340C22×C43C2×#13712yes—
341C22×C43C23×D411yescharacteristic
342C2×D43—22no—
343C2×D43—28no—
344C2×D43—22no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—84no—
349C2×D43C2×#13714yes—
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43—42no—
356C4×C43#53712yes—
357C4×C43C2×H(5,𝔽2)11yescharacteristic
358C4×C43C2×2−1+411yescharacteristic
359Dic43—22no—
360Dic43—22no—
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364Dic43C2×#13514yes—
365C2×#533—431no—
366C2×#529—431no—
367#3248—4316no—
368C2×#479—431no—
369C2×#479D4311yescharacteristic, complemented
370C2×#475—431no—
371C2×#474—431no—
372C2×#467—431no—
373C2×#467—431no—
374C2×#465—431no—
375C2×#465—431no—
376C2×#464—431no—
377C2×#464—431no—
378C2×#462—431no—
379C2×#461—431no—
380C22×C4⋊C8—431no—
381C2×C43#324814yescomplemented
382C2×C43C2×#53711yescharacteristic
383C2×C43C22×#13511yescharacteristic
384C2×C43C22×#13711yescharacteristic
385D43—24no—
386D43—82no—
387C22×Q16—431no—
388C22×Q16—431no—
389C22×SD16—431no—
390C22×SD16—431no—
391C23×C8—431no—
392C23×C8—431no—
393#533—438no—
394#533—864no—
395C2×C4⋊Q8—431no—
396C2×C4⋊Q8—431no—
397#529—438no—
398#529—864no—
399C2×#126—861no—
400C2×#125—861no—
401C2×#125C2×D4311yescharacteristic
402C2×#124—431no—
403C2×#123—861no—
404C2×C22⋊Q8—431no—
405C2×C22⋊Q8—431no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8—861no—
408C2×#121—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×Q8—861no—
412C2×C4×Q8C2×D4311yescharacteristic
413C2×C4×D4—431no—
414C2×C4×D4—861no—
415C2×#117—861no—
416C2×#117—861no—
417C22×C42—431no—
418#479—438no—
419#479C2×D4318yescomplemented
420#475—438no—
421#474—438no—
422#467—438no—
423#467—438no—
424#465—438no—
425#465—438no—
426#464—438no—
427#464—438no—
428#462—438no—
429#461—438no—
430C2×#107—431no—
431C2×#107C2×D4311yescharacteristic
432C2×#106—431no—
433C2×#106C2×D4311yescharacteristic
434C2×C4⋊C8—431no—
435C2×C4⋊C8—431no—
436C2×C4⋊C8—431no—
437C2×C4⋊C8—438no—
438C2×C4⋊C8C2×D4311yescharacteristic
439C2×#103—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#103—431no—
443C2×#103C2×D4311yescharacteristic
444C2×#103C2×D4311yescharacteristic
445C2×#102—431no—
446C2×#102—431no—
447C43C2×#324811yescharacteristic, complemented, Sylow
448C22×Q8—431no—
449C22×Q8—431no—
450C22×Q8—861no—
451C22×Q8C22×D4311yescharacteristic
452C22×D4—431no—
453C22×D4—861no—
454C23×C4—431no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—861no—
458C2×Q16—434no—
459C2×Q16—434no—
460C2×Q16—1722no—
461C2×Q16—1722no—
462C2×SD16—434no—
463C2×SD16—434no—
464C2×SD16—1722no—
465C2×SD16—1722no—
466C22×C8—431no—
467C22×C8—431no—
468C22×C8—434no—
469C22×C8—434no—
470C22×C8—1722no—
471C22×C8—1722no—
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474C4⋊Q8—434no—
475C4⋊Q8—434no—
476C4⋊Q8—862no—
477C4⋊Q8—862no—
478#126—868no—
479#125—22no—
480#125—868no—
481#125C22×D4314yes—
482#124—434no—
483#124—862no—
484#123—868no—
485C22⋊Q8—434no—
486C22⋊Q8—434no—
487C22⋊Q8—434no—
488C22⋊Q8—862no—
489C22⋊Q8—862no—
490C22⋊Q8—868no—
491C22⋊Q8—862no—
492#121—434no—
493#121—862no—
494C4×Q8—22no—
495C4×Q8—434no—
496C4×Q8—434no—
497C4×Q8—868no—
498C4×Q8—862no—
499C4×Q8—862no—
500C4×Q8C22×D4314yes—
501C4×D4—434no—
502C4×D4—862no—
503C4×D4—868no—
504#117—868no—
505#117—868no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—21no—
529C2×C42—431no—
530C2×C42—431no—
531C2×C42—431no—
532C2×C42—434no—
533C2×C42—434no—
534C2×C42—861no—
535C2×C42—861no—
536C2×C42C22×D4311yescharacteristic
537#107—434no—
538#107C22×D4314yes—
539#106—434no—
540#106C22×D4314yes—
541C4⋊C8—434no—
542C4⋊C8—434no—
543C4⋊C8—434no—
544C4⋊C8C22×D4314yes—
545#103—434no—
546#103—434no—
547#103—434no—
548#103—434no—
549#103C22×D4314yes—
550#103C22×D4314yes—
551#102—434no—
552#102—434no—
553C24—431no—
554C24—861no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—432no—
559C2×Q8—432no—
560C2×Q8—864no—
561C2×Q8—861no—
562C2×Q8—861no—
563C2×Q8—862no—
564C2×Q8—862no—
565C2×Q8—862no—
566C2×Q8—862no—
567C2×Q8—1724no—
568C2×Q8C23×D4312yes—
569C2×D4—432no—
570C2×D4—864no—
571C2×D4—861no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—1724no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—434no—
583C22×C4—434no—
584C22×C4—432no—
585C22×C4—432no—
586C22×C4—864no—
587C22×C4—864no—
588C22×C4—864no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—1724no—
595C22×C4D4×D4311yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598Q16—1724no—
599Q16—1724no—
600SD16—1724no—
601SD16—1724no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—432no—
605C2×C8—432no—
606C2×C8—862no—
607C2×C8—862no—
608C2×C8—1724no—
609C2×C8—1724no—
610C2×C8C23×D4312yes—
611C2×C8C23×D4312yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—432no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—861no—
627C4⋊C4—864no—
628C4⋊C4C23×D4312yes—
629C4⋊C4C23×D4312yes—
630C4⋊C4C23×D4312yes—
631C22⋊C4—864no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C42—24no—
639C42—434no—
640C42—432no—
641C42—434no—
642C42—432no—
643C42—864no—
644C42—864no—
645C42D4×D4312yes—
646C42C23×D4312yes—
647C23—434no—
648C23—432no—
649C23—862no—
650C23—862no—
651C23—862no—
652C23—1722no—
653C23—1722no—
654C23—1722no—
655C23C2×D4×D4311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—862no—
660Q8—862no—
661Q8—862no—
662Q8—862no—
663Q8—1728no—
664Q8—1722no—
665Q8—1722no—
666D4—862no—
667D4—862no—
668D4—1728no—
669D4—1722no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—434no—
681C2×C4—432no—
682C2×C4—432no—
683C2×C4—432no—
684C2×C4—868no—
685C2×C4—868no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—864no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—1728no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4C2×D4×D4312yes—
699C2×C4C2×D4×D4312yes—
700C2×C4C2×D4×D4311yescharacteristic
701C2×C4#1306337112yes—
702C2×C4#1306337312yes—
703C2×C4C24×D4311yescharacteristic
704C8—22no—
705C8—22no—
706C8—862no—
707C8—862no—
708C22—434no—
709C22—862no—
710C22—862no—
711C22—868no—
712C22—3444no—
713C22—1722no—
714C22—1722no—
715C22—1722no—
716C22#1458347912yes—
717C22#135×D4312yes—
718C22#137×D4312yes—
719C22C22×D4×D4311yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—434no—
727C4—862no—
728C4—862no—
729C4—1722no—
730C4—1722no—
731C4—1722no—
732C4#1458347912yes—
733C4C2×#1306337111yescharacteristic
734C4C2×#1306337311yescharacteristic
735C2—864no—
736C2—3442no—
737C2#1914593114yesdirect product factor
738C2C2×#1458347911yescharacteristic
739C2C2×#135×D4311yescharacteristic
740C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenterC2×#479D43
hypocenterC43C2×#3248
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14583453C2semidirect
3. #19145931C2direct (N × H)
4. C2×#14583203C2semidirect
5. C2×#14583183C2semidirect
6. C2×#14583178C2semidirect
7. C2×#14583141C2semidirect
8. C2×#14583139C2semidirect
11. C2×#14583122C2semidirect
12. C2×#14583121C2semidirect
13. C2×#14583108C2semidirect
14. C2×#14583103C2semidirect
15. C2×C4⋊C8×D43C2semidirect
16. C2×C43×#479C2semidirect
24. #14583453C22semidirect
46. #14583203C22semidirect
47. #14583183C22semidirect
48. #14583178C22semidirect
49. #14583141C22semidirect
50. #14583139C22semidirect
53. #14583122C22semidirect
54. #14583121C22semidirect
55. #14583108C22semidirect
56. #14583103C22semidirect
62. C4⋊C8×D43C22semidirect
71. C43×#479C22semidirect
369. C2×#479D43semidirect
381. C2×C43#3248semidirect
419. #479C2×D43semidirect
447. C43C2×#3248semidirect
737. C2#19145931direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145834532
C2×#145834342
#191459312
C2×#145832032
C2×#145831832
C2×#145831782
C2×#145831412
C2×#145831392
C2×#145831312
C2×#145831292
C2×#145831222
C2×#145831212
C2×#145831082
C2×#145831032
C2×C4⋊C8×D432
C2×C43×#4792
C2×#324843